Question 1191911
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Physically, when a stone is dropped into a still pond sending out a circular ripple of the radius r = r(t), 


the rate  {{{(dr)/(dt)}}}  is constant and is equal to the speed of surface wave.


The area of the circle is a quadratic function of time, in this case.



So, in reality, the radius r= r(t) and the area A = A(t) are different types of functions, distinct of described in this problem.



You may find many Internet sources, related to this phenomenon.